I’d say that having three different words for “because” increases nuance. As the link to merriam-webster’s article pointed out, you get a nuance of formality between “because” and “as”; “as” is somewhat more formal. I’m not sure if there’s another nuance between “because” and causal “since” but smart money is on there being one (if you survey the use of the two I bet you will find there are very subtle differences of usage there – there almost always are nuances of difference between supposedly synonymous words, even if they’re only differences like level of formality).
Since reading your comment I’ve noted that I don’t use since and because interchangably. I believe because puts emphasis on the reason, while the main focus when using since still lays on the thing being explained.
“I take the left here, since that route is shorter.” – (Slight) stress on the first part, the latter is “just” a justification.
– “Why do you take the right when the left route is shorter?” – “I don’t take the left because it is shorter.” Stress on the last part, it’s the main point of that sentence.
